Introduction to Eruption Forecasting
Marzocchi, Sandri, and Selva, BET_EF: a probabilistic tool for long- and short-term eruption forecasting, Bull. Volcan., 70, 623 632, DOI:10.1007/s00445-007-0157-y, 2008

One of the major goals of modern volcanology is to set up sound risk-based decision-making in land-use planning and emergency management. One of the basic scientific ingredients to achieve these goals is a reliable and quantitative long- and short-term eruption forecasting (EF).

Despite the fact that some recent research on short-term forecasting (from hours to a few days) is based on a deterministic approach (e.g., Voight and Cornelius 1991; Kilburn 2003; see also Hill et al. 2001), the presence of complex and different precursory patterns for distinct eruptions, as well as the exigency to consider the possibility that a precursory pattern does not necessarily lead to an eruption, suggests that a probabilistic approach could be more efficient in EF (e.g., Sparks 2003). In reference to this, it is worth remarking that the probabilistic approach is not incompatible with the deterministic approach, because the former can include deterministic rules as case limit, i.e., when the probability is close to one. In other words, the probabilistic approach is certainly more general, and it also has the advantage of being applicable at different time scales. For instance, during a quiet period of the volcano, EF is estimated by accounting for the past activity of the volcano (long-term EF; see, e.g., Marzocchi and Zaccarelli 2006; Jaquet et al. 2006). Conversely, during unrest, the method allows mid- to short-term EF to be estimated by considering different patterns of pre-eruptive phenomena (e.g., Newhall and Hoblitt 2002; Aspinall and Woo 1994; Aspinall et al. 2003; and Marzocchi et al. 2004).

The concept of short/long-term EF deserves further explanations. The terms "short" and "long" refer to the expected characteristic time in which the process shows significant variations; in brief, during unrest the time variations occur in time scales much shorter than the changes expected during a quiet phase of the volcano. On the other hand, these terms are not linked to the forecasting time window (for instance, we can use a forecasting time window of 1 day for both short- and long-term EF). The distinction between these two time scales, besides the reflecting of a difference in the physical state of the volcano (quiescence and unrest), is also important in a practical perspective. In fact, for example, the long-term EF is a primary component of long-term (years to decades) volcanic hazard assessment that allows different kinds of hazards (volcanic, seismic, industrial, floods, etc.) in the same area to be compared; this comparison is very useful for cost/benefit analysis of risk mitigation actions, and for appropriate land-use planning and location of settlements. In contrast, monitoring mid- to short-time scales assists with actions for immediate vulnerability (and risk) reduction, for instance through evacuation of people from dangerous areas (Fournier d'Albe 1979).

In general, we can say that a realistic EF is usually complicated by the scarce number of data and the relatively poor knowledge of the physical pre-eruptive processes. Overall, this makes any EF hypothesis/model hard to test, also in a backward analysis, for explosive volcanoes. On the other hand, the extreme risk posed by many volcanoes forces us to be pragmatic and attempt to solve the problem from an "engineering" point of view; by this, we mean that the devastating potential of volcanoes close to urbanized areas forces the scientific community to address the issue as precisely as possible. This is best done by treating scientific uncertainty in a fully structured manner and, in this respect, Bayesian statistics is a suitable framework for producing eruption forecasting (and volcanic hazard/risk assessments) in a rational, probabilistic form (e.g., UNESCO 1972; Gelman et al. 1995). In order to illustrate the general philosophy of the approach, we quote Toffler (1990) who said "it is better to have a general and incomplete model, subject to revision and correction, than to have no model at all". We add that the model has to be necessarily "accurate", i.e., without significant biases, because a biased estimation would be useless in practice. On the other hand, the model has to be as "precise" as possible (i.e., the relative error has to be as small as possible), but "precision" has not to be achieved at the expense of "accuracy". In other words, the model may have low "precision", reflecting our scarce knowledge of some physical processes involved.

Model BET_EF: Bayesian Evnet tree for Eruption Forecasting

We address the EF issue by implementing a general quantitative model for volcanic hazard assessment based on the Bayesian event tree (BET). BET represents a development of the method proposed by Marzocchi et al. (2004) based on the event tree (Newhall and Hoblitt 2002) scheme. Specifically, BET follows the philosophy of approach described by Marzocchi et al. (2004), and it proposes some significant novelties like the introduction of the fuzzy approach, the inclusion of a node for the vent location, and an improvement of the statistics formalism. It also contains few minor conceptual changes and implementations. Finally, we put forward a scheme of a software package (BET_EF: Bayesian event tree for eruption forecasting) to calculate the probability of eruption for a generic volcano. It is worth noting that our procedure overlaps some with the Bayesian belief network (BBN) adopted by Aspinall et al. (2003), and, in general, they share the same philosophy. As a matter of fact, both methods deal with multiple parameters monitoring, and with uncertainties. The main difference is that the Bayesian approach of BET allows aleatory and epistemic uncertainties to be directly accounted for in a structured and explicit fashion.

A detailed discussion on the approach adopted for BET_EF can be found in Marzocchi et al. (2004, 2006a, 2008), Newhall and Hoblitt (2002), and Gelman et al. (1995). Here, we report the main features of BET that can be summarized in four general points:

For more info, please visit the BET (Bayesian Event Tree) website.